%%
%% The LaTeX Companion, 3ed
%%
%% Example 11-3-5 on page II-156 in "amsmath, mathtools, cases --- Some case environments".
%%
%% Copyright (C) 2022 Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%%
%% See https://www.latex-project.org/lppl.txt for details.
%%

\documentclass{tlc3examargin}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{207.0pt}

%StartShownPreambleCommands
\usepackage{amsmath}
%StopShownPreambleCommands

\begin{document}
\begin{equation}    P_{r - j} =
 \begin{cases}
    0   &  \text{if $r - j$ is odd,} \\
    r! \, (-1)^{(r - j)/2}
        &  \text{if $r - j$ is even.}
 \end{cases}             \end{equation}
\end{document}
